Mathematical models have been used for over five decades in industrial heat-treating operations. Most of these modeling efforts have emanated from academia or research institutes, with the primary approach of mathematically capturing heat-treating processes and validating quality predictions. In this article, a contrarian but more realistic scenario is considered, where two industrial problem descriptions become the starting point. The technical complexity of the industry problem has been elaborated for a deeper understanding of the issue along with elaboration of the approach and potential methods for determining a solution. Then, quantitative analyses of practical industrial problems are demonstrated. Finally, the potential shift in these approaches with the advent of Industry 4.0 is outlined.

This article discusses the two major applications of hot isostatic pressing (HIP), such as healing of inherent internal defects in castings and welds, and consolidation of powder materials. It describes the design principles of the HIP tooling, as well as the problems associated with mathematical modeling of HIP. The article presents an example for the modeling process of the HIP. It reviews the numerical modeling and tooling design of a casing component demonstration.

Integrated computational materials engineering refers to the use of computer simulations that integrate mathematical models of complex metallurgical processes with computer models used in component and process design. This article outlines an example of a computer-aided engineering tool, such as virtual aluminum castings (VAC), developed and implemented for quickly developing durable cast aluminum power train components. It describes the procedures for the model development of the VAC system. These procedures include linking the manufacturing process to microstructure, linking microstructures to mechanical properties, linking material properties to performance prediction, and model validation and integration into the engineering process. The article discusses the benefits of the VAC system in process selection, process optimization, and improving the component design criteria.

Open-die forging can be distinguished from most other types of deformation processes in that it provides discontinuous material flow as opposed to continuous flow. This article describes the equipment and auxiliary tools used in open-die forging. It discusses the production and practice of open-die forging, with some practical examples. The article illustrates macrosegregation in a large steel ingot and lists the forgeable alloys. It reviews the physical and mathematical models used in deformation modeling. The article explains the contour forging and roll planishing process. It inform that to ensure that forgings can be machined to correct final measurements, it is necessary to establish allowances, tolerances, and specifications for flatness and concentricity. The article also tabulates the allowances and tolerances for as-forged shafts and bars.

Electromagnetic problem solutions are based on the macroscopic theory of the continuous model for the electromagnetic field (EMF). It is described by a system of integral or partial differential equations for five vector quantities, namely, electric field strength, electric flux density, current density, magnetic field strength, and magnetic flux density. This article describes the behavior of the EMF by Maxwell's equations in integral or differential forms. It discusses the definition of potentials; methods of mathematical modeling; boundary conditions; and energy, power density, and electromagnetic forces.

This article provides an overview of steel gear heat treating processes and brings out the nuances of the various important heat treating considerations for steel gear applications. The heat treatment processes covered are annealing, carburizing, hardening, low-pressure carburizing, induction hardening, through hardening, and nitriding. In view of the emerging use of mathematical modeling and optimization, a brief overview of its application for process and design optimization is also provided.

Crevice corrosion is a form of localized corrosion that affects many alloys that normally exhibit passive behavior. This article discusses the frequently used crevice corrosion testing and evaluation procedures. These procedures include specific crevice corrosion tests, multiple-crevice assembly tests, cylindrical materials and products evaluation, component testing, electrochemical tests, and mathematical modeling.

Temperature is a typical parameter characterizing the heating level of any particle belonging to a heated body. The basic problem of heat transfer computation is associated with appropriate determination of heat transfer coefficients. This article provides a discussion on the basic equations, initial and boundary conditions, and multiple reflection phenomena of mathematical modeling. These boundary conditions include the Dirichlet, Neumann, and Henkel conditions.

Designing of induction heating, or, generally electro technological installations, requires mathematical modeling for solving problems related to various physical phenomena, including electromagnetic (EM), thermal, mechanical, fluidic, and metallurgical fields. This article focuses on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method.

This article provides a discussion on adhesively bonded joints and elastic-plastic mathematical model for an adhesive in shear. It discusses the design rules for thin bonded structures and reviews computer programs for the highly loaded stepped-lap joints. The article describes the two-dimensional effects associated with load redistribution around flaws and with damage tolerance. The elastic-isotropic geometric stress-concentration factors and empirically established correlation factors of mechanically fastened joints are discussed. The article provides information on the identification of optimal joint proportions for single-row joints, and the design and analysis of the stronger multirow joints, with particular regard to the bearing-bypass interaction.

This article describes two principal methods for detecting well casing corrosion, namely, metal-loss tools and casing current measurement, as well as their limitations and advantages. It discusses the factors to be considered in designing well casing cathodic protection systems. These include the determination of cathodic protection current by the casing polarization and CPP tests or by mathematical models; calculation of casing-to-anode separation; isolation of the casing from other facilities; consideration of stray current interference from other dc power sources; and determination of the size and the location of the anode bed for effective current output for the desired life of the anode bed. The article concludes with a discussion on the commissioning and monitoring of cathodic protection systems.

The field of bioprinting is a subset of additive manufacturing (AM) that is rapidly expanding to meet the needs of regenerative medicine and tissue engineering. Bioprinting encompasses a broad spectrum of issues, from cell expansion and novel bioink development to cell/stem cell printing, from organoid-based tissue organization to bioprinting of human-scale tissue structures, and from building cell/tissue/organ-on-a-chip to biomanufacturing of multicellular engineered living systems. This article focuses on two challenges regarding bioprinting: bioinks and crosslinking. It describes the methods for characterizing the performance of bioink formulations and the effectiveness of crosslinking strategies. The topics covered include modalities of bioprinting, characteristics of bioink, rheological properties of bioink sols, rheological measurements, mathematical models of bioink rheology, postfabrication polymer network mechanics, mechanical properties of crosslinked bioinks, and printability of bioinks. Finally, specific strategies used for crosslinking bioinks, as well as some emerging strategies to further improve bioinks and their crosslinking, are summarized.

Gas quenching is one of the standard quenching technologies used in fabricating metallic components. The gas quenching process is usually performed at elevated pressures and is therefore mostly referred to as high-pressure gas quenching (HPGQ). This article presents the physical principles of HPGQ and also presents the equipment for gas quenching. The article describes the three types of gas that are mainly used for HPGQ: nitrogen, helium, and argon. It provides the mathematical model for heat fluxes and temperatures during HPGQ. The article also presents typical industrial applications for HPGQ in addition to equipment process and safety.

This article focuses on the general methods and approaches from the perspective of a reconstruction analyst and includes discussions relevant to materials failure analysts at the incident scene. The elements of accident reconstruction are described. These have conceptual similarity with the principles for failure analysis of material incidents that are less complex than a large-scale accident. The article provides a brief review of some general concepts on the use of modeling which can be a very powerful tool for information pertaining to the reconstruction of an accident where the model can be a physical, mathematical, or logical representation of a physical system or process.

This article provides guidelines for the assessment of model quality in materials science and engineering. It discusses the fundamentals of model quality assessment and the calibration of mechanistic material models. The article reviews the considerations for the model verification during software implementation planning to identify suitable programs, software components, and programming languages. It describes the validity tests used in model validation, including boundary-value tests, degenerate problem tests, sensitivity tests, and benchmarking. The article also presents an example of model calibration, verification, and validation for the prediction of martensite start temperature of steels.

This article provides a brief historical perspective, a classification of metallurgical processes, basic model development efforts, and an overview of the potential future directions for the modeling of metals processing. It describes the classification of material behavior models, which can be grouped broadly into three classes: statistical, phenomenological, and mechanistic models. The article also presents an overview of the potential directions for the modeling of metals processing.

This article provides a comprehensive review and critical assessment of numerical modeling of heat and mass transfer in fusion welding. The different fusion welding processes are gas tungsten arc welding, gas metal arc welding, laser welding, electron beam welding, and laser-arc hybrid welding. The article presents the mathematical equations of mass, momentum, energy, and species conservation. It reviews the applications of heat transfer and fluid flow models for different welding processes. Finally, the article discusses the approaches to improve reliability of, and reduce uncertainty in, numerical models.